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Negotiable préavis?
What's in your working contract?
There had been some changes to labor law in the past years.
You can always negotiate. Many (perhaps most) employers do not want to keep someone who is only interested in moving on.
As KASSEISTAMPER notes above, with two willing parties, anything is negotiable. There is nothing stopping you asking. Many employers would be happy to come to some agreement so that you leave on good terms.
However, they are also perfectly within the law not to enter into a negotiation with you.